Question
If x2a = y2b =z2c ≠
0 and x2 = yz, then the value of (ab + bc + ca) /bc is :Solution
x 2a =y2b =z2c =k x 2a =k x =(k)2a y =(k)1/2b z =(k) 1/2b x 2 =yz ((k) 1/2b )2=(k) 1/2b (k) 1/2b (k) 1/a = (k) 1/2b + 1/2b 1/a = 1/2b + 1/2c By adding 1/2a both sides, 1/a +1/ 2a =1/ 2a +1/ 2b +1/ 2c 3/2a = (ab + bc + ac) /2abc (ab + bc + ac) /bc = 3
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